Vernam Cipher and Perfect secrecy

  1. Prove that if only a single character is encrypted, then the shift cipher is perfectly secret.
  2. What is the largest plaintext space M you can find for which the mono-alphabetic substitution cipher provides perfect secrecy? (Note: M need not contain only valid English words.)
  3. Show how to use the Vigenere cipher to encrypt any word of length t so that perfect secrecy is obtained (Note: you can choose the length of the key).